Angel Gutierrez and Adela Jaime: Research on the Teaching of Mathematics to Talented and Gifted Students

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The international mathematics education research on mathematically talented students includes several broad directions: Identification of students, design of adequate mathematics learning activities or environments, and description of attributes of these students’ thinking. In this lecture, we shall present an overview of the main research results on mathematically talented students, related to the mentioned directions, we have obtained during last years.

Our research in this area has three different focuses: One is to design a tool to validate the adequacy of mathematical tasks used in the classroom, in terms of cognitive demand and van Hiele levels of reasoning. A second focus is the design of activities useful both for average and talented students in their ordinary classroom. We have explored the use of dynamic geometry software in some of these activities. A third focus is to learn how talented students approach mathematics, to identify their processes of learning and differential thinking characteristics.

Finally, we shall make an overview of other Spanish research groups and the main actions taken in Spain to promote mathematically talented students.